Advances in Applied Clifford Algebras
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Transition from three to four dimensions in the differential-form formulation of electrodynamics
Advances in Applied Clifford Algebras - Tập 11 Số S2 - Trang 127-153 - 2001
Construction of a Few Quantum Mechanical Hamiltonians via Lévy-Leblond Type Linearization: Clifford Momentum, Spinor States and Supersymmetry
Advances in Applied Clifford Algebras - Tập 32 - Trang 1-13 - 2022
A number of new Lévy-Leblond type equations admitting four component spinor
solutions have been proposed. The pair of linearized equations thus obtained in
each case lead to Hamiltonians with characteristic features like L-S coupling
and supersymmetry. The relevant momentum operators have often been understood in
terms of Clifford algebraic bases producing Schrödinger Hamiltonians with L-S
couplin...
The generalized clifford-hermite continuous wavelet transform
Advances in Applied Clifford Algebras - Tập 11 - Trang 219-231 - 2001
Specific wavelet kernel functions for a continuous wavelet transform in
Euclidean space are constructed in the framework of Clifford analysis. Their
relationship with the heat equation and a newly introduced wavelet differential
equation is established.
(Para-) Kähler Structures on $$\rho $$ ρ -Commutative Algebras
Advances in Applied Clifford Algebras - - 2018
Erratum to: Some Matrix Representations of Fibonacci Quaternions and Octonions
Advances in Applied Clifford Algebras - - 2017
Décomposition canonique des rotations
Advances in Applied Clifford Algebras - Tập 12 - Trang 97-100 - 2002
Hyperbolic multi-topology and the basic principle in quantum mechanics
Advances in Applied Clifford Algebras - Tập 9 - Trang 109-118 - 1999
In this paper, applying the direction strangeness of the hyperbolic space-time,
we introduce the double metric space and the multi-topological structure, and in
the wave-particle topology, we give one kind of imaginary metric representation
for light-quantum hypothesis, uncertainty principle, energy level transition and
interference conditions, etc. in quantum mechanics.
Two Novel Algebraic Techniques for Quaternion Least Squares Problems in Quaternionic Quantum Mechanics
Advances in Applied Clifford Algebras - Tập 26 - Trang 169-182 - 2015
Quaternion least squares (QLS) problem is one method of solving overdetermined
sets of quaternion linear equations $${AX \approx B}$$ and $${AXC \approx B}$$
that are appropriate when there are errors in the matrix B. This paper, by means
of complex representation and real representation of a quaternion matrix,
studies the QLS problems, and derives two new algebraic techniques for finding
solution...
Brownian Motion, Martingales and Itô Formula in Clifford Analysis
Advances in Applied Clifford Algebras - Tập 32 - Trang 1-18 - 2022
Clifford analysis has been the field of active research for several decades
resulting in various methods to solve problems in pure and applied mathematics.
However, the area of stochastic analysis has not been addressed in its full
generality in the Clifford setting, since only a few contributions have been
presented so far. Considering that the tools of stochastic analysis play an
important role ...
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